Arboriculture & Urban Forestry 36(1): January 2010 For compaction measurements, an appropriate apparatus would be a nucleodensimeter. However, this piece of equipment requires specific expertise and a special operating permit as it is a nuclear device. To meet the objective of low-technology, an analog soil compaction gauge was tested as the sole device for penetration resistance assessment. In each sampled tree pit, four measures were taken, at each specified depth. To be able to compare results between tree pits, soil texture and moisture level must be similar. For that reason, particle-size analysis was carried out in the soil laboratory with the hydrometer method. Soils were classified as sandy loam or loamy sand. No direct soil moisture measurements were taken during field work. Accordingly, to make certain that soil moisture levels in tree pits were comparable when penetra- tion resistance was measured, rainfall bulletins were checked at the end of field work. If there was any rainfall within five days prior to a collection date (data not presented), then the collected information was discarded. Consequently, the July 11, July 13, and August 24 data were rejected for analysis. The discarded sam- ples accounted for 3% of the total (48 samples / 1,532 samples). Because of the presence of urban canyons in the experimental design, the assessment of light levels on sampled trees was pri- oritized. In order to obtain local solar irradiation information, one possibility was to acquire data from climate stations. Although they provide reliable radiation records, they usually record ra- diation only for horizontal surfaces. Additionally, extrapolation of measurements from these collection sites to experimenta- tion zones is difficult because, in practice, site-specific factors are difficult to remove from the original data (Flint and Childs 1987). Another option was to use existing algorithms model- ing solar radiation (Annandale 2004; Bauerle et al. 2004; Groot 2004). Yet, most of these are very detailed models that did not suit the user-friendly needs of City of Montreal arboriculture practitioners. Therefore, a computer-programmed model was developed to automatically estimate the number of hours of ir- radiation on street trees and transfer this information to the data- base and the local geographic information system (Jutras 2008). Input data for the model were latitude, longitude, Julian cal- endar, sunrise and sunset information per day; street orientation and width; mean height of adjacent and opposite buildings in a 50 m (164 ft) radius (arbitrary radius of influence); distance from tree to adjacent and opposite buildings; tree mid-crown elevation (calculated from morphological data) and position of tree pit on street. This information was combined using trigo- nometric formulae to compute irradiation values by minute per daytime. Output results were summarized into hourly, total daily, and seasonal irradiation per tree. Supplemental computa- tions were carried out for a standardized 4 m (13 ft) height to estimate tree pit potential irradiation for newly transplanted trees of ball & burlap size. All irradiation levels were estimated from May 1 (normal earliest date of budburst: Hunter and Lechow- icz 1992) to August 15 (end of active vegetative growth for northern trees: Harris and Bassuk 1995). Model output results were validated by collecting field data at specific times dur- ing 2003 and 2004 by ecological zone, size and height of trees. Inevitably, such a model introduces bias as the estima- tion does not take into account parameters like intensity of di- rect beam radiation, amount of diffuse radiation, absorbed radiation, obstructed/unobstructed sky, or nearby building- reflected radiation. Nevertheless, it was hypothesized the model might be accurate enough to measure the impact of 3 reduced irradiation on urban tree growth as radiation calcula- tions were transformed in five classes for the statistical analy- sis, hence eluding the need for an intricate model (next section). In this experimental design, every tree was consid- ered as a unit thus obviating the problems associated with subjective partitioning of the studied system into homo- geneous zones. In order to do so, biophysical param- eters were always collected in relation to a single tree. Statistical Analysis Contingency analysis is an interesting procedure to estimate de- pendence among descriptors that are not in monotonic relation- ship, or among qualitative descriptors. Tree-related data have such mathematical characteristics. In this research, contingency analysis was used to assess the relationship between urban tree growth and various states of local abiotic variables. Accord- ingly, prior to contingency analysis, the study authors searched for differential growth classes by using multivariate intermedi- ate linkage clustering and correspondence analysis, the latter be- ing a nonparametric principle component analysis (Jutras 2008). Clustering is a useful tool when the description of surveyed individuals is multidimensional. Its goal is to partition a set of n individuals into groups, called clusters, such that the individu- als in each group are more similar to each other than to those in other groups (Friedman and Meulman 2004). Inputs for the clustering analysis were DBH, crown diameter, height, crown diameter / DBH, crown volume / DBH, height / DBH, crown volume, annual DBH increment, crown diameter increment, height increment, and crown volume increment. Outputs were species-specific groups with distinctive growth patterns. For this study, the detection of a maximum of four different clusters, from slow-growing to fast-growing trees, was sought in order that a robust classification model be deployed over the City of Mon- treal urban tree database. The final classifications were the fol- lowing: Norway maple (3 growth groups); silver maple (3); hack- berry (4); green ash (4); honeylocust (4); and Siberian elm (4). Concurrently to this procedure, quantitative abiotic data were transformed into classes as required for contingency analysis. The conversion was accomplished by segmenting quantities into sub- sets representative of encountered ecological conditions (Table 1). Irradiation was divided into five classes; street width was subdi- vided into three classes: narrow (mostly residential), intermediate (encompassing all zone coding types), wide and very wide streets (commercial and institutional zones); nutrient subset classes were determined according to benchmark recommendations (Ministère de l’Agriculture et de l’Alimentation de l’Ontario 2003); counts of aerial and underground obstacles were converted to presence/ absence input. Surficial geomorphologic deposits associated with each tree location were classified into three types: 1) silty till and stony silty till, 2) clay and silty clay, and 3) sand and gravel. The contingency analysis was carried out not only for every species but also on a combined all-species matrix. This research objective was to test model generalization. Species differed by their morphological characteristics and distribution of age classes among sampling sites, therefore potentially introducing high variability in the model algorithm. Consequently, if sig- nificant relationships between tree growth classes and certain abiotic parameters can be found, then a general model might be conceived. The all-species matrix was constructed to give ©2010 International Society of Arboriculture
January 2010
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